To find when the line does not intersect the curve, set the equations equal to each other:

\(x^2 - 4x + c = 2x - 7\)

Rearrange to form a quadratic equation:

\(x^2 - 6x + c + 7 = 0\)

For the line not to intersect the curve, the quadratic equation must have no real roots. This occurs when the discriminant is less than zero:

\(b^2 - 4ac < 0\)

Here, \(a = 1\), \(b = -6\), and \(c = c + 7\). Calculate the discriminant:

\((-6)^2 - 4(1)(c + 7) < 0\)

\(36 - 4(c + 7) < 0\)

\(36 - 4c - 28 < 0\)

\(8 - 4c < 0\)

\(8 < 4c\)

\(c > 2\)